This set of Aptitude Questions and Answers (MCQs) focuses on “Functions”.

1. Given log 3 = 0.4771, then what would be the value of (log (0.27)^{2} * log (27 / 10)^{2/3}) / (log 9)?

a) 0.2887

b) -0.4526

c) -0.3427

d) 0.1996

View Answer

Explanation: Given log 3 = 0.4771.

(log (0.27)

^{2}* log (27 / 10)

^{2/3}) / (log 9) = (2(log (27 / 100)) * 2 / 3 log (27 / 10)) / 2 log 3

= (2(log 3

^{3}– log 10

^{2}) * 2 / 3 (log 3

^{2}– log 10)) / 2 log 3

= (2(3 log 3 – 2 log 10) * 2 / 3 (3 log 3 – log 10)) / 2 log 3

Substituting value of log 3 as given,

= (2(3 * 0.4771 – 2) * 2 / 3 (3 * 0.4771 – 1)) / 2 * 0.4771

= (2 * (- 0.5687) * 2 / 3 (0.4313)) / 0.9542

= (- 1.1374 * 0.2875) / 0.9542

= -0.3427

2. Given the value of log 2 = 0.3010, then what would be the value of log_{5}512?

a) 3.876

b) 2.457

c) 1.786

d) 4.924

View Answer

Explanation: log

_{5}512 = log

_{10}512 / log

_{10}5

= log

_{10}2

^{9}/ log

_{10}(10 / 2)

= 9log

_{10}2 / (log

_{10}10 – log

_{10}2)

= ((9 * 0.3010) / (1 – 0.3010))

= 2.709 / 0.699

= 3.876

3. Which of the following relationship between x and y would satisfy log(x / y) + log(y / x) = log (x + y)?

a) x – y = 1

b) x + y = 1

c) x / y = 1

d) x * y = 1

View Answer

Explanation: Given,

log(x / y) + log(y / x) = log (x + y)

➩ log ((x / y) * (y / x)) = log (x + y)

➩ log 1 = log (x + y)

➩ 1 = x + y

4. What would be the value of the expression (1 / log_{2}80) + (1 / log_{4}80) + (1 / log_{10}80)?

a) 1

b) 2

c) 4

d) 8

View Answer

Explanation: (1 / log

_{2}80) + (1 / log

_{4}80) + (1 / log

_{10}80) can be written as,

➩ log

_{80}2 + log

_{80}4 + log

_{80}10

➩ log

_{80}80

➩ 1

5. Which value of z given in the options below would satisfy log_{z} (5 / 7) = 1 / 3?

a) 15 / 21

b) 343 / 125

c) 125 / 343

d) 21 / 15

View Answer

Explanation: Given,

log

_{z}(5 / 7) = 1 / 3

➩ z

^{1/3}= 5 / 7

➩ ∛z = 5 / 7

➩ z = (5 / 7)

^{3}

➩ z = 125 / 343

6. Which of the following options is the correct value for log_{6} ((46656) (216) / (36))?

a) 3

b) 36

c) 6

d) 7

View Answer

Explanation: Given, log

_{6}((46656) (216) / (36)).

➩ log

_{6}((6

^{6})(6

^{3}) / (6

^{2}))

➩ log

_{6}(6

^{7})

➩ 7 log

_{6}6

➩ 7 * 1

➩ 7

7. Given log_{10}x = y, then how can 10^{3y} be expressed in terms of x?

a) x^{3}

b) x^{2} / 2

c) 3x^{3}

d) 3x^{3} / 2

View Answer

Explanation: Given,

log

_{10}x = y

➩ 10

^{y}= x

➩ 10

^{3y}= (10

^{y})

^{3}= x

^{3}

8. Which set of values of z satisfy log (z^{2} – 6z + 6) = 0?

a) 1 and 2

b) 4 and 6

c) 5 and 1

d) 3 and 2

View Answer

Explanation: Given,

log (z

^{2}– 6z + 6) = 0

➩ z

^{2}– 6z + 6 = 10

^{0}

➩ z

^{2}– 6z + 6 = 1

➩ z

^{2}– 6z + 5 = 0

➩ z

^{2}– 5z – 1z + 5 = 0

➩ z(z – 5) + (- 1) (z – 5) = 0

➩ Thus, z = 1 and 5 satisfies the equation.

9. Which of the following options represent the same value as log 0.234?

a) log 2.34 + 1

b) log 2.34 – 1

c) log 2.34 / 100

d) – log 2.34

View Answer

Explanation: Given, log 0.234

➩ log 0.234 = log (2.34 / 10)

= log 2.34 – log 10

= log 2.34 – 1

10. Solve log (a – 13) + 3log2 = log (3a + 1) and tell which of the following options state the correct value of a?

a) 21

b) 24

c) 20

d) 25

View Answer

Explanation: Given,

log (a – 13) + 3log2 = log (3a + 1)

➩ log (a – 13) + log2

^{3}= log (3a + 1)

➩ log (a – 13) + log8 = log (3a + 1)

➩ log (8a – 104) = log (3a + 1)

➩ 8a – 104 = 3a + 1

➩ 5a = 105

➩ a = 105 / 5

➩ a = 21

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